CN104765272A - Four-rotor aircraft control method based on PID neural network (PIDNN) control - Google Patents

Abstract

The invention discloses a four-rotor aircraft control method based on PID neural network (PIDNN) control. First, dynamic equations of a four-rotor aircraft are established based on the Newton-Euler equations, and then, a nested controller is proposed. An inner loop decentralized controller is designed based on a PIDNN method to realize attitude control, and the outer loop adopts a classical PID control method. Next, online learning of a PIDNN controller is realized by an error back propagation method, the connection initial weight of PIDNN is determined based on the principle of PID control, and an appropriate learning step is selected according to the discrete Lyapunov theory to guarantee the convergence of the controller. Thus, the control problem of a four-rotor aircraft caused by high degree of nonlinearity, strong coupling and under-actuating capability, disturbance from the external environment in the process of flight and other factors can be effectively solved.

Description

A kind of quadrotor control method based on PID neural network control (PIDNN)

Technical field

The present invention relates to aircraft automatic control technology field, is the flight control realizing quadrotor based on PID neural network control (PIDNN) method.

Background technology

Quadrotor, as the one in VUAV series, obtains in military and civilian field and applies more and more widely.Compare fixed wing aircraft, quadrotor has the characteristic such as low-latitude flying, spot hover.Compared to traditional helicopter, quadrotor has that structure is simple, mobility strong, volume are little, cost is low and the characteristic such as good concealment.These characteristics make quadrotor to fly in limited space to high efficient and reliable.

Quadrotor is made up of fuselage and four rotors, as shown in Figure 1.Power is provided by four rotors, and rotor is divided into two groups: (1,3) and (2,4), turns to contrary, to offset the aerodynamic force moment of torsion produced because of rotor wing rotation.Control (1,3) rotating speed organizing rotor can the angle of pitch of control system along y-axis and the translation along x-axis, control (2,4) rotating speed organizing rotor can the roll angle of control system along x-axis and the translation along y-axis, changes the translation of rotating speed energy control system along z-axis of four rotors simultaneously.Only have 4 driving forces due to quadrotor but needed the motion of 6 degree of freedom, therefore it is the nonlinear system of a drive lacking, strong coupling, and its impact by external disturbance is larger.So the research controlled the flight of quadrotor becomes the key problem of research, and the quality of controller performance affects the flight quality of quadrotor to a great extent.The present invention is based on the control method that PID neural network control (PIDNN) proposes a kind of quadrotor, controlling to realizing good flight.

Summary of the invention

The object of the invention is to the flight control problem solving quadrotor, propose a kind of control method controlled based on PID neuroid (PIDNN), to improving the flight quality of quadrotor.

For achieving the above object, the present invention proposes following technical scheme: a kind of control method controlled based on PID neuroid (PIDNN), it comprises the steps:

S1: the kinetic model setting up quadrotor.

Assuming that quadrotor is rigid body and structure full symmetric, set up earth axes E={E _x, E _y, E _zand body axis system B={B _x, B _y, B _z, as shown in Figure 1.Set up the kinetic model of quadrotor by newton-Eulerian equation, model comprises x, the translation equation in y, z tri-directions and roll angle φ, the rotation equation in pitching angle theta and crab angle ψ tri-directions.

Wherein, S (.)=sin (.), C (.)=cos (.), m is the quality of quadrotor, I _xx, I _yy, I _zzbe respectively the moment of inertia in three directions, J _rbe the moment of inertia of rotor, g is acceleration of gravity, U ₁, U ₂, U ₃, U ₄for control vector, be defined as follows:

$\left[\begin{array}{c}{U}_1\\ U_2\\ U_3\\ U_4\end{array}\right]=\left[\begin{array}{c}b({{\mathrm{\Ω}}_1}^2+{{\mathrm{\Ω}}_2}^2+{{\mathrm{\Ω}}_3}^2+{{\mathrm{\Ω}}_4}^2)\\ b(-{{\mathrm{\Ω}}_2}^2+{{\mathrm{\Ω}}_4}^2)\\ b({{\mathrm{\Ω}}_1}^2-{{\mathrm{\Ω}}_3}^2)\\ d({{\mathrm{\Ω}}_1}^2-{{\mathrm{\Ω}}_2}^2+{{\mathrm{\Ω}}_3}^2-{{\mathrm{\Ω}}_4}^2)\end{array}\right]$

Wherein, b and d is respectively tension coefficient and the resistance coefficient of rotor.U ₁the controlled quentity controlled variable of rotor lift, U ₂the controlled quentity controlled variable of roll angle φ, U ₃the controlled quentity controlled variable of pitching angle theta, U ₄it is the controlled quentity controlled variable of crab angle ψ;

S2, be quadrotor CONTROLLER DESIGN, this controller forms by inner and outer ring is nested.Outer shroud is position and height controller, and adopt classical PID to control, inner ring is gesture stability, adopts Decentralized PID neuroid (PIDNN) to control; Control system architecture as shown in Figure 2.The motion of outer ring position is determined by inner ring attitude angle.Height controller is according to object height z _daltitude control amount U is calculated with present level position z ₁, positioner is according to target location x simultaneously _d, y _din conjunction with current location x, y Converse solved go out object attitude angle φ _dand θ _dimport attitude controller into, then attitude controller draws rolling, pitching and driftage controlled quentity controlled variable U ₂, U ₃, U ₄reach kinetic model, finally, kinetic model calculates in conjunction with the impact of wind field the state that this time walks system, is back to the calculating that each controller carries out step in lower a period of time.

(1) design height PID controller.

By the height equation in kinetics equation, lift control amount U can be released ₁:

$U_1=\frac{m}{C_{\mathrm{\φ}}{C}_{\mathrm{\θ}}}(P_z+g)$

In formula, C _φc _θ≠ 0, P _zfor height PID controller, form is as follows:

$P_z=k_{\mathrm{zP}}(z_d-z)+k_{\mathrm{zI}}\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\mathrm{ts}\×(z_{\mathrm{di}}-z_i)+k_{\mathrm{zD}}({\stackrel{\·}{z}}_d-\stackrel{\·}{z})$

In formula, k _zP, k _zIand k _zDbe the ratio of controller respectively, integration and differentiation coefficient, k is iterations, walks when ts is.

(2) design attitude PID controller.

By U ₁bring the equation in x and the y direction in kinetic model into, and think that ψ is very little and be approximately 0, can obtain:

P _x＝(P _z+g ₁)tanθ

P _y＝-(P _z+g ₁)tanφ

The PID controller in design x, y direction is:

$P_x=k_{\mathrm{xP}}(x_d-x)+k_{\mathrm{xI}}\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\mathrm{ts}\×(x_{\mathrm{di}}-x_i)+k_{\mathrm{xD}}({\stackrel{\·}{x}}_d-\stackrel{\·}{x})$

$P_y=k_{\mathrm{yP}}(y_d-y)+k_{\mathrm{yI}}\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\mathrm{ts}\×(y_{\mathrm{di}}-y_i)+k_{\mathrm{yD}}({\stackrel{\·}{y}}_d-\stackrel{\·}{y})$

(3) attitude PIDNN controller is designed.

The PIDNN controller of roll angle is three layers of feed-forward network, and be made up of input layer, hidden layer and output layer, network structure as shown in Figure 3.

● input layer

Input layer has two neuron x ₁=φ (k) and x ₂=φ _dk (), φ (k) is roll angle actual value, φ _dk () is roll angle setting value, wherein, k is iterations.

● hidden layer

Hidden layer is the most important level embodying PIDNN controller function, comprises three neurons, is respectively ratio unit, integration unit and Differential Elements, their input u _j(k) be:

$u_j\left(k\right)=\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}\left(k\right)\·x_i\left(k\right),j=\mathrm{1,2,3}$

In formula, w _ijk () is for input layer is to the connection weight of hidden layer.Three neuronic outputs are respectively:

$o_1\left(k\right)=u_1\left(k\right)=\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{w}_{i1}\left(k\right)x_i\left(k\right)$

$o_2\left(k\right)=u_2\left(k\right)+o_2(k-1)=\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{w}_{i2}\left(k\right)x_i\left(k\right)+o_2(k-1)$

$o_3\left(k\right)=u_3\left(k\right)-u_3(k-1)=\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{w}_{i3}\left(k\right)x_i\left(k\right)-\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{w}_{i3}(k-1)x_i(k-1)$

● output layer

Output layer only comprises a neuron, completes the output function of network, and output quantity is the controlled quentity controlled variable U of roll angle ₂(k):

$U_2\left(k\right)=\underset{j=1}{\overset{3}{\mathrm{\Σ}}}{w}_j^{\′}\left(k\right)o_j\left(k\right)$

In formula, w ' _jk () is for hidden layer is to the connection weight of output layer.

S3, by error back propagation method, realizes the on-line study of PIDNN controller, to adjust the connection weight of neural network.

The on-line learning algorithm of PIDNN controller adopts error back propagation method.This algorithm, based on gradient descent method, by the amendment to network weight weight values, reaches the object making objective function E (k) value minimum.Objective function E (k) is defined as:

$E\left(k\right)=\frac{1}{2}{e_{\mathrm{\φ}}}^2\left(k\right)$

In formula, e _φ(k)=φ _dk error amount that ()-φ (k) is roll angle.On-line learning algorithm is described below:

Hidden layer to output layer weight iterative formula is:

w′ _j(k+1)＝w′ _j(k)-η _j·Δw′ _j(k)

η _jfor w ' _jlearning Step.According to back propagation algorithm, in formula, weight increment can be expressed as:

$\mathrm{\Δ}{w}_j^{\·}\left(k\right)=\frac{\∂E\left(k\right)}{\∂w_j^{\·}\left(k\right)}=\frac{\∂E\left(k\right)}{\∂U_2\left(k\right)}\frac{\∂U_2\left(k\right)}{\∂w_j^{\′}\left(k\right)}=\frac{\∂E\left(k\right)}{\∂e_{\mathrm{\φ}}\left(k\right)}\frac{\∂e_{\mathrm{\φ}}\left(k\right)}{\∂\mathrm{\φ}\left(k\right)}\frac{\∂\mathrm{\φ}\left(k\right)}{\∂U_2\left(k\right)}\frac{\∂U_2\left(k\right)}{\∂w_j^{\′}\left(k\right)}$

Order $\mathrm{\δ}\left(k\right)=\∂\mathrm{\φ}\left(k\right)/\∂U_2\left(k\right),$ Can try to achieve:

Δw′ _j(k)＝-e _φ(k)o _j(k)δ(k)

Input layer to hidden layer weight iterative formula is:

w _ij(k+1)＝w _ij(k)-η _i·Δw _ij(k)

η _ifor w _ijlearning Step.In formula, weight increment can be expressed as:

$\mathrm{\Δ}{w}_{\mathrm{ij}}\left(k\right)=\frac{\∂E\left(k\right)}{\∂w_{\mathrm{ij}}\left(k\right)}=\frac{\∂E\left(k\right)}{\∂U_2\left(k\right)}\frac{\∂U_2\left(k\right)}{\∂o_j\left(k\right)}\frac{\∂o_j\left(k\right)}{\∂u_j\left(k\right)}\frac{\∂u_j\left(k\right)}{\∂w_{\mathrm{ij}}\left(k\right)}$

Formula before comprehensive, can obtain:

Δw _ij(k)＝-e _φ(k)w′ _j(k)x _i(k)δ(k)

S4, by selecting suitable connection weight initial value and Learning Step, ensures the stability of PIDNN controller.

(1) selection of connection weight initial value

With reference to the feature of classical PID controller, determine the initial value of PIDNN controller connection weight.Choosing input layer to the connection weight initial value of hidden layer is:

w _1j＝+1,w _2j＝-1,j=1,2,3

Choosing hidden layer to the connection weight initial value of output layer is:

w′ ₁＝K _P,w′ ₂＝K _I,w′ ₃＝K _D

In formula, K _pfor scale-up factor, K _ifor integral coefficient, K _dfor differential coefficient.

(2) selection of Learning Step

Based on discrete Lyapunov's theory, select connection weight step-length:

Hidden layer is to output layer:

$0<{\mathrm{\&eta;}}_j<\frac{8}{{\left[o_j\left(k\right)\mathrm{\&delta;}\left(k\right)\right]}^2}$

Input layer is to hidden layer:

$0<{\mathrm{\&eta;}}_i<\frac{8}{{\left[w_j^{\&prime;}\left(k\right)x_i\left(k\right)\mathrm{\&delta;}\left(k\right)\right]}^2}$

The PIDNN controller architecture of roll angle as shown in Figure 4, the angle of pitch and the controller of crab angle and the substantially identical of roll angle.Suitable initial value chosen to each attitude angle controller and utilizes discrete Lyapunov function to judge convergence, the error of each attitude angle system can be made to level off to zero, and then ensureing the stability of whole system.

Accompanying drawing explanation

Fig. 1 is the structure diagram of quadrotor;

Fig. 2 is controller architecture figure;

Fig. 3 is the PIDNN controller network structural drawing of roll angle;

Fig. 4 is the PIDNN controller architecture figure of roll angle;

Fig. 5 is control system hardware block diagram;

Fig. 6 is the PCB of control system;

Fig. 7 is the quadrotor model machine built;

Fig. 8 is the experimental result of quadrotor track;

Fig. 9 is the experimental result of quadrotor attitude angle.

Embodiment

Below in conjunction with accompanying drawing of the present invention and example, clear, complete description is carried out to the technical scheme of the embodiment of the present invention.

The present invention has built quadrotor model machine, and the control method that the present invention proposes has been applied in the control system of this quadrotor.The main modular of control system comprises main controller module, sensor assembly, navigation module, motor control module, communication module and data acquisition module etc., and hardware configuration as shown in Figure 5.

Main controller module: the i.e. core processor of flight control system, it is the core control portions of whole system, the attitude angular rate (pitch rate, rolling angle rate and yawrate) that primary responsibility pick-up transducers detects, the linear acceleration of three axles and course information, and real-time resolving; According to the flight information detected, in conjunction with set control program, calculate and export controlled quentity controlled variable; Carried out the transmission of data by wireless communication module and land station, realize receive control command change of flight state and under pass Flight Condition Data.The present invention adopts 8 AVR microcontroller ATMEGA2560-16AU to be system master chip.

Sensor assembly: mainly comprise Inertial Measurement Unit, barometer, electronic compass etc.Inertial Measurement Unit adopts six axle Inertial Measurement Unit MPU6000, is integrated with 3 axle MEMS gyro instrument, 3 axle mems accelerometers, and an extendible digital moving processor DMP, in order to resolve the flight attitude of quadrotor.Barometer adopts the barometer module MS5611 of MEAS company, to measure the current exact height of quadrotor.Electronic compass selects the triple axle digital compass HMC5883L of Honeywell Inc., to carry out pose calibrating to inertial navigation system.

Navigation module: adopt high-precision GPS navigation, module master chip is U-BLOX, can revise and solidify baud rate, and interior tape storage can preserve setting.This module can provide quadrotor current latitude and longitude information, flight path direction and ground velocity information etc.

Motor control module: comprise 4 brushless electric machines and 1 four-in-one electron speed regulator.Main controller module exports control signal to electron speed regulator, and then electron speed regulator controls the rotating speed of 4 motors according to the control signal obtained, thus the control of the lift realized 4 rotors generations and torque.

As shown in Figure 6, the quadrotor model machine built as shown in Figure 7 for the PCB of control system.

In order to verify the control program that the present invention proposes, the quadrotor model machine built is utilized to carry out the experiment of spot hover.Make quadrotor keep hovering at the height of 2m, experimental result as shown in FIG. 8 and 9.Can be seen by result, the track in quadrotor x, y and z tri-directions can control in dbjective state, and oscillation amplitude is all no more than 0.1m; Actual attitude angle also can follow the change of setting value preferably; Steady-state error, the hyperharmonic vibration of track and attitude angle are all less, and quadrotor can realize the hovering at desired location preferably.Can draw by experiment: controller proposed by the invention has good performance, the demand that quadrotor system flight controls can be met.

Technology contents of the present invention and technical characteristic have disclosed as above; but those of ordinary skill in the art still may do all replacement and the modification that do not deviate from spirit of the present invention based on teaching of the present invention and announcement; therefore; scope should be not limited to the content that embodiment discloses; and various do not deviate from replacement of the present invention and modification should be comprised, and contained by present patent application claim.

Claims (5)

1., based on a quadrotor control method for PID neural network control, it is characterized in that comprising:

S1: the kinetic model setting up quadrotor;

S2, be quadrotor CONTROLLER DESIGN, this controller forms by inner and outer ring is nested.Outer shroud is position and height controller, and adopt classical PID to control, inner ring is gesture stability, adopts Decentralized PID neuroid (PIDNN) to control;

S3, by error back propagation method, realizes the on-line study of PIDNN controller, to adjust the connection weight of neural network;

S4, by selecting suitable connection weight initial value and Learning Step, ensures the stability of PIDNN controller.

2. according to the method shown in claim 1, it is characterized in that: the mode setting up the kinetic model of quadrotor in described S1 is:

Set up the kinetic model of quadrotor by newton-Eulerian equation, model comprises x, the translation equation in y, z tri-directions and roll angle φ, the rotation equation in pitching angle theta and crab angle ψ tri-directions.

Wherein, S (.)=sin (.), C (.)=cos (.), m is the quality of quadrotor, I _xx, I _yy, I _zzbe respectively the moment of inertia in three directions, J _rbe the moment of inertia of rotor, g is acceleration of gravity, U ₁, U ₂, U ₃, U ₄for control vector, be defined as follows:

Wherein, b and d is respectively tension coefficient and the resistance coefficient of rotor.U ₁the controlled quentity controlled variable of rotor lift, U ₂the controlled quentity controlled variable of roll angle φ, U ₃the controlled quentity controlled variable of pitching angle theta, U ₄it is the controlled quentity controlled variable of crab angle ψ.

3. according to the method shown in claim 1, it is characterized in that: the mode for quadrotor CONTROLLER DESIGN in described S2 is:

(1) design height PID controller.

By the height equation in kinetics equation, lift control amount U can be released ₁:

In formula, C _φc _θ≠ 0, P _zfor height PID controller, form is as follows:

In formula, k _zP, k _zIand k _zDbe the ratio of controller respectively, integration and differentiation coefficient, k is iterations, walks when ts is.

(2) design attitude PID controller.

By U ₁bring the equation in x and the y direction in kinetic model into, and think that ψ is very little and be approximately 0, can obtain:

P _x＝(P _z+g ₁)tanθ

P _y＝-(P _z+g ₁)tanφ

The PID controller in design x, y direction is:

(3) attitude PIDNN controller is designed.

The PIDNN controller of roll angle is three layers of feed-forward network, is made up of input layer, hidden layer and output layer.

● input layer

Input layer has two neuron x ₁=φ (k) and x ₂=φ _dk (), φ (k) is roll angle actual value, φ _dk () is roll angle setting value, wherein, k is iterations.

● hidden layer

Hidden layer is the most important level embodying PIDNN controller function, comprises three neurons, is respectively ratio unit, integration unit and Differential Elements, their input u _j(k) be:

In formula, w _ijk () is for input layer is to the connection weight of hidden layer.Three neuronic outputs are respectively:

● output layer

Output layer only comprises a neuron, completes the output function of network, and output quantity is the controlled quentity controlled variable U of roll angle ₂(k):

In formula, w ' _jk () is for hidden layer is to the connection weight of output layer.

4. according to the method shown in claim 1, it is characterized in that: the mode of the on-line study of PIDNN controller in described S3 is:

The on-line learning algorithm of PIDNN controller adopts error back propagation method.This algorithm, based on gradient descent method, by the amendment to network weight weight values, reaches the object making objective function E (k) value minimum.Objective function E (k) is defined as:

In formula, e _φ(k)=φ _dk error amount that ()-φ (k) is roll angle.On-line learning algorithm is described below:

Hidden layer to output layer weight iterative formula is:

w′ _j(k+1)＝w′ _j(k)-η _j·Δw′ _j(k)

η _jfor w ' _jlearning Step.

Input layer to hidden layer weight iterative formula is:

w _ij(k+1)＝w _ij(k)-η _i·Δw _ij(k)

η _ifor w _ijlearning Step.

5. according to the method shown in claim 1, it is characterized in that: in described S4, select the mode of suitable connection weight initial value and Learning Step to be:

(1) selection of connection weight initial value

With reference to the feature of classical PID controller, determine the initial value of PIDNN controller connection weight.Choosing input layer to the connection weight initial value of hidden layer is:

w _1j＝+1,w _2j＝-1,j=1,2,3

Choosing hidden layer to the connection weight initial value of output layer is:

w′ ₁＝K _P,w′ ₂＝K _I,w′ ₃＝K _D

In formula, K _pfor scale-up factor, K _ifor integral coefficient, K _dfor differential coefficient.

(2) selection of Learning Step

Hidden layer to the connection weight Learning Step of output layer is:

Input layer to the connection weight Learning Step of hidden layer is:

。